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II. DISCREPANCIES IN THE
NEWTONIAN UNIVERSE

But even while this neat, orderly scheme of the
universe was being eagerly incorporated into Victorian
philosophical and social concepts, its very basis was

being undermined by experimental and observational
data, and by logical analysis in four different realms
of physics and astronomy: in the realm of optics, the
experiments of Michelson and Morley on the speed of
light were to destroy the Newtonian concepts of abso-
lute space and time and to replace them by the Ein-
steinian space-time concept (the special theory of rela-
tivity); in the realm of radiation, the discoveries of the
properties of the radiation emitted by hot bodies were
to upset the Maxwell wave-theory of light and to
introduce the quantum theory (the photon) with its
wave-particle dualism; in the realm of observational
astronomy, the discrepancy between the deductions
from Newtonian gravitational theory and the observed
motion of Mercury (the advance of its perihelion)
indicated the need for a new gravitational theory
which Einstein produced in 1914 (the general theory
of relativity); finally, in the realm of cosmology, var-
ious theoretical analyses showed that the nine-
teenth-century models of the universe, constructed
with Newtonian gravitational theory and space-time
concepts, were in serious contradiction with stellar
observations.

Although the investigation of each of these depar-
tures from classical physics is of extreme importance
and each one has an important bearing on the most
recent cosmological theories, we limit ourselves here
to the cosmological realm and, where necessary in our
discussion, use the results of modern physics without
concern about how they were obtained. However,
before we discuss the difficulties inherent in Newtonian
cosmology, we must consider one other important
nineteenth-century discovery which, at the time,
seemed to have no bearing on the structure of the
universe but which ultimately played a most important
role in the development of cosmology. This was the
discovery of the non-Euclidean geometries by Gauss,
Bolyai, Lobachevsky, Riemann, and Klein. At the time
that these non-Euclidean geometries were discovered,
and for many years following, scientists in general
considered them to be no more than mathematical
curiosities, with no relevance to the structure of the
universe or to the nature of actual space. Most mathe-
maticians and scientists simply took it for granted
that the geometry of physical space is Euclidean and
that the laws of physics must conform to Euclidean
geometry.

This attitude, however, was not universal and Gauss
himself, the spiritual father of non-Euclidean geometry,
proposed a possible (but in practice, unrealizable) test
of the flatness of space by measuring the interior angles
of a large spatial triangle constructed in the neigh-
borhood of the earth. Also, the mathematician W. K.
Clifford, in The Common Sense of the Exact Sciences
(1870; reprint, New York, 1946), speculated that the
geometry of actual space might not be Euclidean. He
proposed the following ideas: (1) that small portions
of space are, in fact, of a nature analogous to little
hills on a surface which is, on the average, flat—
namely, that the ordinary laws of geometry are not
valid in them; (2) that this property of being curved
or distorted is continually being passed on from one
portion of space to another after the manner of a wave;
(3) that this variation of the curvature of space is what
really happens in that phenomenon which we call
motion of matter, whether ponderable or ethereal; (4)
that in the physical world nothing else takes place but
this variation, subject (possibly) to the laws of con-
tinuity.

Clifford summarized his opinion as follows:

These were, indeed, prophetic words, for, as we shall
see, in the hands of Einstein the non-Euclidean geome-
tries became the very foundation of modern cosmo-
logical theory. But let us first examine the flaws and
difficulties inherent in the Newtonian cosmology of the
nineteenth century.